The two adjacent sides of a rectangle are $2 x^{2} - 5 x y + 3 z^{2}$ and $4 x y - x^{2} - z^{2}$ . Find its perimeter

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Solution

Let $a$ and $b$ be two adjacent sides of rectangle.
Then we know perimeter of rectangle will be $2 (a + b)$ .
Here two adjacent sides are $2 x^{2} - 5 x y + 3 z^{2}$ and $4 x y - x^{2} - z^{2}$ .
Thus perimeter $=$ $2 (a + b) = 2 (2 x^{2} - 5 x y + 3 z^{2} + 4 x y - x^{2} - z^{2})$
$= 2 (x^{2} + 2 z^{2} - x y)$
$= 2 x^{2} + 4 z^{2} - 2 x y$

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